7-1-1_q15.ipynb

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    "## 7-1-1　予想問題\n",
    "### 問15\n",
    "次のプログラム中の【　a　】と【　b　】に入れる正しい答えの組合せを，解答群の中から選べ。ここで，配列の要素番号は1から始まる。\n",
    "\n",
    "　k-近傍法（k-Nearest Neighbor Algorithm, k-NN）は，分類や回帰問題を解くための教師あり学習アルゴリズムである。k-NNアルゴリズムは，新しいデータ点に対して最も近いk個の既知のデータ点を用いて予測を行う。具体的には，既知のデータ点と新しいデータ点間の距離を計算し，最も近いk個のデータ点のラベルを用いて，新しいデータ点のラベルを決定する。  \n",
    "　関数kNearestNeighborsは，既知のデータ点の2次元配列trainDataとそのラベルの配列trainLabelから，新しいデータ点dataに対して最も近いk 個のデータ点を求め，新しいデータ点のラベルを返す。ここでデータ点は，2次元データを扱うこととする。  \n",
    "　関数kNearestNeighborsで使う関数powは，第1引数として正の実数aを，第2引数として実数bを受け取り，aのb乗の値を実数型で返す。\n",
    "\n",
    "〔プログラム〕  \n",
    "Pythonでは配列（リスト）の要素番号は0から始まるので，要素番号をすべて1ずらすよう修正"
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    "def kNearestNeighbors(trainData, trainLabel, data, k):\n",
    "    itemRank = [None] * k\n",
    "    distRank = [None] * k\n",
    "    labelList = []\n",
    "    labelCount = []\n",
    "    # trainDataの距離を計算し，近いものからk個を選出\n",
    "    x = data[0]\n",
    "    y = data[1]\n",
    "    for i in range(len(trainData)):\n",
    "        xi = trainData[i][0]\n",
    "        yi = trainData[i][1]\n",
    "        dist = pow(pow(x - xi, 2) + pow(y - yi, 2), 0.5)\n",
    "        j = 0\n",
    "        while (itemRank[j] != None and distRank[j] > dist):\n",
    "            j = j + 1\n",
    "        if (itemRank[j] == None or j == k):\n",
    "            itemRank[j] = i\n",
    "            distRank[j] = dist\n",
    "        elif (j < k):\n",
    "            for m in range(k - 1, j, -1): # range関数部分が空欄a（初期値，終了値，増分）\n",
    "                itemRank[m] = itemRank[m - 1]\n",
    "                distRank[m] = distRank[m - 1]\n",
    "            itemRank[j] = i\n",
    "            distRank[j] = dist\n",
    "    \n",
    "    # 距離の近いデータについて，ラベルを数える\n",
    "    for i in range(len(itemRank)):\n",
    "        t = trainLabel[itemRank[i]]\n",
    "        j = 0\n",
    "        while (j < len(labelList) and t != labelList[j]): # andより後が空欄b\n",
    "            j = j + 1\n",
    "        if (j < len(labelList)):\n",
    "            labelCount[j] = labelCount[j] + 1\n",
    "        else:\n",
    "            labelList.append(t)\n",
    "            labelCount.append(1)\n",
    "\n",
    "    # 最も数の多いラベルを data のラベルとする\n",
    "    label = labelList[0]\n",
    "    count = labelCount[0]\n",
    "    for i in range(1, len(labelList)):\n",
    "        if (labelCount[i] > count):\n",
    "            label = labelList[i]\n",
    "            count = labelCount[i]\n",
    "    return label"
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